Poincar\'e inequality and the Lp convergence of semi-groups
Probability
2010-03-25 v2 Functional Analysis
Abstract
We prove that for symmetric Markov processes of diffusion type admitting a "carr\'e du champ", the Poincar\'e inequality is equivalent to the exponential convergence of the associated semi-group in one (resp. all) spaces for . Part of this result extends to the stationary non necessarily symmetric situation.
Cite
@article{arxiv.1003.0784,
title = {Poincar\'e inequality and the Lp convergence of semi-groups},
author = {Patrick Cattiaux and Arnaud Guillin and Cyril Roberto},
journal= {arXiv preprint arXiv:1003.0784},
year = {2010}
}